Implementation Study of Implicit Uncertainty Propagation (iup) in Decomposition-based Optimization

In previous work we have developed and implemented a mathematical construct referred to as “Implicit Uncertainty Propagation (IUP)” for estimating uncertainties within the bilevel optimization framework of collaborative optimization (CO). The implicit uncertainty estimates were used to develop a robust collaborative optimization framework, which is capable of managing design constraint variations, to ensure robust feasibility of the optimal design. In this research we present a basic error analysis for the IUP method, hence providing a guideline for the effective implementation of the IUP strategy. It is also recognized in this paper that the application of IUP is not limited to bilevel optimization framework of CO only. In fact, it can be utilized in any decomposition-based optimization framework (such as SAND) where disciplinary sensitivity information is available. In addition, the IUP method can be employed to estimate the objective function variations in such decomposition-based optimization frameworks, which enable the inclusion of robust objective functions in the framework if desired. Two multidisciplinary test problems, implemented in the CO and SAND frameworks respectively, are used to verify the applicability of the IUP method.